Equilibrium catch

Recall the stock net growth expression. When the net growth is zero, the natural growth of the stock equals the harvest and a biological equilibrium is established. The intersections between the blue lines and the green curve gives five such equilibriums and infinitely many more could be obtained. The red curve and line to the right represent the collection of the infinite number of biological equilibriums obtained by an infinite number of different fishing efforts.

The long term catch equation is obtained when inserting the catch-effort long term relationship, H(E, X)= H(E, X(E)) = H(E). This equation has some useful properties in order to connect to the economics of fisheries, as the unexplained variable (fishing effort) is closely related to the cost side of fishing, while the explained variable (harvest) gives the fishing revenue.

Adding economics

Assume a constant unit price of fishing and a constant unit cost of fishing, p. The total revenue in equilibrium is

TR(E) = p H(E)

Similarly assume a constant unit cost of fishing effort, a. a comprises all costs, including opportunity costs of the all factors employed in production. By that the cost equation includes the demand of a normal profit. The total cost is

TC(E) = a E

Since the normal profit is included as opportunity costs of production factors, the difference between total revenue and total costs is abnormal profits. In the case of alinear cost equation (as here) and a homogeneous fleet, all the abnormal profit isresource rent:

Pi(E) = TR(E) - TC(E)

The decision makers

Open access has to be studied as a situation of having many independent decision makers fishing on the same stock resource. We have been assuming a homogeneous fleet with respect of technical and economic efficiency. Now let each fishing effort unit represent each decision maker. Since all decision makers are facing the same stock situation at the same time, the revenue of each decision maker will be the average revenue

AR(E) = TR(E)/E

The cost of each decision maker is in general given by the marginal cost

MC(E) = dTC/dE

which in the case of a linear cost equation is

MC = a

The decision maker (e.g. fisher) is indifferent between fishing of moving the input factors in production (labour and capital) to the best alternative placement when

AR = MC

as this situation provides the fisher with a normal profit from the fishing activity.

If AR > MC one should expect more fishers to enter the fishery, as they will earn a profit exceeding the normal level in the fishery. By the same kind of reasoning AR < MC will lead to decision makers leaving the fishery, as a higher profit could be earned by placing the input factors elsewhere.

The reasoning above shows that AR = MC really represents the open access equilibrium where a large number of independent decision makers freely chose to enter or exit the fishery. This equilibrium is also referred to as the bioeconomic equilibrium, the combined biological equilibrium () and economic equilibrium ()

The relation between revenue (blue) and cost (red) is shown in the figure to the left for the whole fishery (above) and for the unit of fishing effort (below). The equilibrium at AR = MC is a stable equilibrium since the effort will increase when AR > MC and decrease when AR < MC.